Problem: On the first 4 quizzes of her physics class, Nadia got an average score of 80. What does she need on the next quiz to have an overall average of 82?
Let her score on the next quiz be $x$ The sum of all of her scores is then $4 \cdot 80 + x$ The same sum must also be equal to $5 \cdot 82$ Solve: $x = 5 \cdot 82 - 4 \cdot 80 = 90$.